I thought AI was declared dead in the 80s of the previous century
Declared dead by who? What were they referring to by AI?
As for the P = NP problem, I found the following description:
A major unsolved problem in computer science is the so-called P=NP problem: machines are considered in which there is a certain amount of freedom in choosing the next step in a computation (such machines are called non-deterministic). By making good guesses (or choices) one can often obtain a quicker computation than by systematically working through all possible cases in a deterministic way. The P == NP problem asks whether every function computable on a non-deterministic machine in polynomial (i.e., tractable) time is computable in polynomial time on ordinary (deterministic) machines.
-- N. J. Cutland, Computability. Cambridge University Press, 1980. p. 238.
Everything that can be invented has been invented. - Charles H. Duell, US Commissioner of Patents, in 1899.
Update: I've found several papers on the subject including Is the NP problem solved?. Haven't had a chance to read through them yet, but they look interesting.
Update 2: A short introduction to quantum computation